A) 10 cm
B) 11 cm
C) 12 cm
D) None of these
Correct Answer: A
Solution :
We know that, perimeter of MBC = 36 cm i.e., \[a+a+AC=36\] i.e., \[2a+2AO=36\] ?(i) Also, perimeter of \[a+AO+BO=24\,cm\] ?(ii) Using Eq. (i), we have \[a+AO=18\] From Eq. (ii), \[BO=6\,cm\] \[\Rightarrow \] \[BD=12\,cm\] Now, in \[\Delta AOB,\] \[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\] \[A{{B}^{2}}-A{{O}^{2}}=36\] \[\Rightarrow \] \[(AB-AO)=2\] i.e., \[a-AO=2\] ?(iii) On solving Eqs. (i) and (ii), we get a = 10 = Side of rhombusYou need to login to perform this action.
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